Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also, find the number of elements of this sample space.

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Solution

Given :
A pair of dice (one is blue and the other red) rolled once.
If a dice is rolled, then the possible outcomes are $(1, 2, 3, 4, 5, 6)$ .
So, if two dice are throw then the possible outcome are
$(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),$
$(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),$
$(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)$
Hence the required sample space is $S = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} (1, 1), & (1, 2), & (1, 3), & (1, 4), & (1, 5), & (1, 6), (2, 1), & (2, 2), & (2, 3), & (2, 4), & (2, 5), & (2, 6) (3, 1), & (3, 2), & (3, 3), & (3, 4), & (3, 5), & (3, 6) (4, 1), & (4, 2), & (4, 3), & (4, 4), & (4, 5), & (4, 6) (5, 1), & (5, 2), & (5, 3), & (5, 4), & (5, 5), & (5, 6) (6, 1), & (6, 2), & (6, 3), & (6, 4), & (6, 5), & (6, 6) \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭$

Number of elements in sample space $= 6 \times 6$
$= 36$ .

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